Question

Why is $3x-3$ reducible over $\mathbb{Z}$?

score 80 · Answer 1 · 2026-04-13 12:33:45

80

Views

Why is $3x-3$ reducible over $\mathbb{Z}$?

Published on 13 Apr 2026 - 12:33

score 96 · Answer 2 · 2022-06-28 20:19:24

96

Views

Consider $p(x,y)=3x^{5}+3y^{4}x^{4}+6xy+3y+12\in\mathbb{Q}[x,y]$. Is $p(x,y)$ irreducible in $\mathbb{Q}[x,y]$? And in $\mathbb{Z}[x,y]$?

Published on 28 Jun 2022 - 20:19

score 84 · Answer 3 · 2022-06-30 06:31:41

84

Views

If $F= {\mathbb{Q}[x]}/{(x^5+5x^2-10)}$ then show that $[F:\mathbb{Q}]=5$.

Published on 30 Jun 2022 - 6:31

score 70 · Answer 4 · 2022-06-30 08:28:52

70

Views

Seperability degree and roots of $f=X^{p^2}-TX^p-T\in\mathbb{F}_p(T)[X]$

Published on 30 Jun 2022 - 8:28

score 129 · Answer 5 · 2026-04-13 03:27:31

129

Views

Is there an irreducible polynomial over $\mathbb{Z}[x]$ with setwise coprime coefficients that is composite for all integer arguments?

Published on 13 Apr 2026 - 3:27

score 145 · Answer 6 · 2026-04-12 08:07:49

145

Views

Maximal and prime ideals in $\mathbb{Z}[x]$

Published on 12 Apr 2026 - 8:07

score 54 · Answer 7 · 2026-04-12 03:55:10

54

Views

The zero polynomial in a commutative ring with unity

Published on 12 Apr 2026 - 3:55

score 42 · Answer 8 · 2026-04-11 21:35:49

42

Views

Irreducibilty (reducibility) of a family of polynomials

Published on 11 Apr 2026 - 21:35

score 166 · Answer 9 · 2022-07-21 17:05:54

166

Views

Irreducible polynomials with distinct irrational roots and all non-zero coefficients

Published on 21 Jul 2022 - 17:05

score 773 · Answer 10 · 2026-04-14 18:41:54

773

Views

Show that every irreducible polynomial in $\mathbb Z_p$ is a divisor of $x^{p^n}-x$ for some $n$.

Published on 14 Apr 2026 - 18:41

score 144 · Answer 11 · 2026-03-25 14:38:00

144

Views

Show irreducibility for Polynomials of degree 4 over p-adic Fields

Published on 25 Mar 2026 - 14:38

score 61 · Answer 12 · 2026-04-03 11:42:36

61

Views

How to obtain $\operatorname{Gal}(f\mid \mathbb{Q}_3)=A_3$ or $S_3$?

Published on 03 Apr 2026 - 11:42

score 38 · Answer 13 · 2026-04-03 11:44:32

38

Views

Show that $x^3-p \in \Bbb{Q}_p[x]$ for $p=2,3$ splits completely or doesnt over $\mathbb{Q}_3$(p^(1/3)) and $\mathbb{Q}_2$(p^(1/3))

Published on 03 Apr 2026 - 11:44

score 89 · Answer 14 · 2022-08-01 12:24:08

89

Views

Irreducible polynomials, mod $m$

Published on 01 Aug 2022 - 12:24

score 104 · Answer 15 · 2026-04-13 19:54:37

104

Views

Were the real irreducible polynomials understood before complex numbers were developed

Published on 13 Apr 2026 - 19:54

List Question

Why is $3x-3$ reducible over $\mathbb{Z}$?

Consider $p(x,y)=3x^{5}+3y^{4}x^{4}+6xy+3y+12\in\mathbb{Q}[x,y]$. Is $p(x,y)$ irreducible in $\mathbb{Q}[x,y]$? And in $\mathbb{Z}[x,y]$?

If $F= {\mathbb{Q}[x]}/{(x^5+5x^2-10)}$ then show that $[F:\mathbb{Q}]=5$.

Seperability degree and roots of $f=X^{p^2}-TX^p-T\in\mathbb{F}_p(T)[X]$

Is there an irreducible polynomial over $\mathbb{Z}[x]$ with setwise coprime coefficients that is composite for all integer arguments?

Maximal and prime ideals in $\mathbb{Z}[x]$

The zero polynomial in a commutative ring with unity

Irreducibilty (reducibility) of a family of polynomials

Irreducible polynomials with distinct irrational roots and all non-zero coefficients

Show that every irreducible polynomial in $\mathbb Z_p$ is a divisor of $x^{p^n}-x$ for some $n$.

Show irreducibility for Polynomials of degree 4 over p-adic Fields

How to obtain $\operatorname{Gal}(f\mid \mathbb{Q}_3)=A_3$ or $S_3$?

Show that $x^3-p \in \Bbb{Q}_p[x]$ for $p=2,3$ splits completely or doesnt over $\mathbb{Q}_3$(p^(1/3)) and $\mathbb{Q}_2$(p^(1/3))

Irreducible polynomials, mod $m$

Were the real irreducible polynomials understood before complex numbers were developed

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